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Studying charge-trapping defects within the siliconlattice of a p-channel CCD using a single-trap“pumping” technique.Journal ItemHow to cite:

Wood, D.; Hall, D.; Murray, N.; Gow, J. and Holland, A. (2014). Studying charge-trapping defects within thesilicon lattice of a p-channel CCD using a single-trap “pumping” technique. Journal of Instrumentation, 9, article no.C12028.

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Studying charge-trapping defects within the siliconlattice of a p-channel CCD using a single-trap“pumping” technique

D. Wooda∗, D.J. Halla, N.J. Murraya, J.P.D. Gowa, A. Hollanda, P. Turnerb and D. Burtb

aCentre for Electronic Imaging,The Open University, Walton Hall, Milton Keynes, MK76AA, UK

be2v Technologies Plc,Chelmsford, Essex, UKE-mail: daniel.wood@open.ac.uk

ABSTRACT: The goals of future space missions such as Euclid require unprecedented positionalaccuracy from the responsible detector. Charge coupled devices (CCDs) can be manufactured withexceptional charge transfer properties; however the harsh radiation environment of space leads todamage within the silicon lattice, predominantly through proton collisions. The resulting latticedefects can trap charge, degrading the positional accuracy and reducing the useful operating timeof a detector. Mitigation of such effects requires precise knowledge of defects and their effects oncharge transfer within a CCD. We have used the technique of single-trap “pumping” to study twosuch charge trapping defects; the silicon divacancy and the carbon interstitial, in a p-channel CCD.We show this technique can be used to give accurate information about trap parameters requiredfor radiation damage models and correction algorithms. We also discuss some unexpected resultsfrom studying defects in this way.

KEYWORDS: CCD, silicon, defect, radiation damage, p-channel, pocket pumping, Euclid.

∗Corresponding author.

Contents

1. Introduction 1

2. Charge-Trapping 2

3. Trap Pumping 3

4. Experimental Results + Discussion 44.1 Identifying Dipoles 44.2 Emission Time Constants 54.3 Discussion 7

5. Conclusions 7

1. Introduction

The long-term effects of radiation damage on any semiconductor material detector can be sep-arated into two distinct classes; surface damage effects resulting from ionization as an impingingparticle passes through the detector, and bulk damage effects which occur due to displacementdamage within the semiconductor lattice [1]. Surface damage leads to increased dark signal andcan cause flat-band voltage shifts and leakage currents within the detector [2], whilst displacementdamage leads to the formation of stable lattice defects which can produce mid-band gap energylevels that degrade detector charge transfer performance [3].

For the case of scientific CCDs surface effects are largely negated by physical radiation hard-ening of the device and the ability to operate with the silicon surface inverted; causing holes (forn-channel devices) or electrons (for p-channel devices) from the column stops to migrate to theSi/SiO2 interface and suppress dark current generation [4]. Bulk effects can also cause dark currentincrease, however the focus of this paper is the degradation of charge-transfer efficiency (CTE) bythe induced lattice defects; if left unaddressed this can significantly reduce the useful operatingtime of a CCD.

The degradation of CTE can be mitigated through the use of iterative post-image correctionalgorithms which simulate charge capture and release by defect energy levels [5]. The accuracyof the model and hence the success of the correction depends on detailed knowledge of the defectparameters; ideally we wish to know exactly the length of time between the capture and emissionof a signal electron (n-channel) or hole (p-channel) at the defect level, which corresponds to theemission time constant of the defect.

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CCDs are increasingly required for very precise measurements; for example the ESA Euclidvisible imager (VIS) instrument will aim to study subtle gravitational lensing effects through shapemeasurements of approximately 1.5 billion galaxies [6][7]. The VIS focal plane will be composedof 36 n-channel CCDs; at present n-channel devices can be produced which exhibit greater CTEand suffer from less dark current generation than comparable p-channel devices [8]. However it isbelieved that for future long-term space missions p-channel CCDs could represent a more radiation-hard alternative to traditional n-channel devices, since the radiation induced hole-capturing defectlevels in a p-channel device may not have such a significant detrimental effect on CTE as theelectron-capturing levels in an n-channel device at the typical operating temperatures and timingsof such missions [8]. To this end, we are here analysing defects within a p-channel CCD with a viewto use of this technology in future scientific applications. Gravitational lensing measurements willrequire highly detailed knowledge of the detector point spread function (PSF) and accurate modelsof the effects of radiation damage on the PSF [9]. In this paper we use the technique of trap pump-ing [10][11][12][13][14] with a p-channel e2v CCD 204 [15] to analyse charge-trapping defectsindividually, with the aim of providing accurate information about defect emission time constantsfor the improvement of radiation damage models and CTE degradation correction algorithms.

2. Charge-Trapping

The capture (recombination) and release (generation) of charge carriers at mid-band gap deeplevels is described by Shockley-Read-Hall (SRH) kinetics, which equates generation and recom-bination rates to form differential equations describing carrier concentrations [16][17]. The elec-tron/hole capture rates at a defect are given by Equations 2.1 and 2.2 where n and p are the electronand hole densities respectively, vth is the thermal velocity of the carriers, and σn,p are the cross-sections for electrons and holes.

cn = nσvth , (2.1)

cp = pσvth , (2.2)

Under steady state conditions Equations 2.3 and 2.4 give the relationship between capture andemission rates, where nT and pT are the SRH densities shown in Equations 2.5 and 2.6 which givethe carrier concentrations when the Fermi level EF coincides with the defect energy level ET interms of Nc and Nv; the densities of states in the conduction band and valence band respectively.

en = cnnT , (2.3)

ep = cp pT , (2.4)

nT = Ncexp(−Ec −ET

kT) , (2.5)

pT = Nvexp(−ET −Ev

kT) , (2.6)

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The above expressions for capture and emission rates lead to Equations 2.7 and 2.8 describingthe capture and emission time constants for a defect of energy ET above the valence band edge(shown for p-channel only since that is the concern of this paper):

τc =1

pσvth, (2.7)

τe =1

Nvσvthexp(

ET

kT) , (2.8)

In this paper we use the method of trap pumping to investigate defect emission time constants andtheir temperature dependence over a small range, with a view to a much larger silicon lattice defectstudy in the near future. There are a vast number of possible stable defects within the silicon lattice,however in this paper we focus on two of those that are known to cause CTE degradation in p-channel CCDs under typical operating conditions: the silicon divacancy and the carbon interstitial.

3. Trap Pumping

Trap pumping works by altering the sequence of the clock phase electrodes within a CCD suchthat a signal charge packet is moved back and forth between two adjacent pixels many times (thenumber of pumping cycles N)[13][14]. Both the image section and serial register of a CCD canbe pumped. Moving charge in this way amplifies the effects of any charge trapping defects withina pixel. Starting with a flat-field exposure the signal is pumped for N cycles and then read outnormally. During each pumping cycle there exists a probability that a defect may capture a sig-nal charge from the charge packet within a given pixel and then release it into an adjacent pixel.Repeating the cycle many times leads to characteristic dipoles within the resulting image at defectlocations, such as those shown in Figure 1.

The capture and emission time constants can be used to model the trapping process and obtainan expression for the dipole intensity. A full explanation of the trap pumping process is outlinedin [10]. To a first approximation we can assume that if a charge carrier comes into contact withan empty trap the capture is instant (in other words τc is negligible compared to τe) leading toEquation 3.1 which describes for a 3-phase CCD the probability per cycle that a given electron ispumped in terms of the period of time for which a charge packet resides beneath a single phaseelectrode; the “phase time”, tph:

Pp = exp(−tph

τe

)− exp

(−2tph

τe

)(3.1)

The e2v CCD204 is in fact a 4-phase device, however for the duration of this study two of thephases were connected together such as to clock the CCD as a 3-phase device. If it is assumed thatthe probability of capture is 100% (providing the trap is empty) then the dipole intensity I is givento a first approximation by I = NPp for N pumping cycles. If the capture probability is not 100%then the intensity is scaled approximately linearly with Pc where Pc is the capture probability for agiven signal level.

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Figure 1: Left - Characteristic dipoles produced in a trap pumped image taken from the imagesection of the device. Each square represents one pixel. Right - Outline of the irradiated regions ofthe e2v CCD204. Due to the split serial register, the whole image area is reproduced by stitchingtogether images from the left and right sections; giving the central region of overscan. Axis labelsshow the pixel number.

By tracking I across a range of tph which surrounds the emission time constant we produce dipoleintensity curves for each defect. Differentiation of the expression for intensity shows that the curvemaximum should lie at ln(2)× τe. Therefore we have a method of directly probing the emissiontime constant parameter space.

4. Experimental Results + Discussion

4.1 Identifying Dipoles

The e2v CCD204 consists of a 4k by 1k pixels image area with a split serial register. Two sub-sections of a CCD204 were irradiated with protons at a total fluence of 2×109 cm−2 and 4×109

cm−2 respectively, for 10 MeV equivalent protons [15] (for reference, the Euclid end of life fluenceis expected to be around 5×109 cm−2)[18]. By 10 MeV equivalent fluence we refer to the fluenceof 10 MeV protons which would cause the same amount of displacement damage, as indicated bythe NIEL scaling hypothesis [?]. The outline of each irradiated region is shown in Figure 1.

A recent study by Mostek et al. [11] outlined three predominant charge trapping defect speciesfor parallel transfer in proton irradiated p-channel silicon; a hole trapping level of the silicon di-vacancy (VV), a carbon interstitial (Ci) and a carbon/oxygen interstitial(CiOi). Using a method oftrap pumping in the temperature domain Mostek estimated the energy levels and cross-sections ofthe defect species, which can then be used to deduce emission time constants for a given temper-ature. The energy levels of the divacancy and carbon interstitial were found to be 0.184± 0.012eV and 0.287± 0.068 eV above the valence band edge respectively [11]. Using the Mostek dataas a guide we chose to probe the divacancy defect at temperatures of -114, -119 and -124 ◦C aswell as the carbon interstitial at temperatures of -93, -97 and-101 ◦C. The reason for omission of

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the carbon/oxygen interstitial from this study is that the emission time constant for that defect ismany times larger than for the divacancy or carbon interstitial. The phase times required would bein the order of seconds, leading to very time consuming measurements and increased issues withaccurate temperature control for the duration of each measurement. The alternative is to operate athigher temperatures, however this would lead to issues with increased dark current.

For measurements at each temperature, a flat field exposure was first taken at approximately25000 holes intensity (equivalent to 25000 e− intensity in an n-channel CCD) before the signal waspumped for 4000 cycles with a given phase time. Small fluctuations in the flat-field signal level donot affect the charge cloud volume within each pixel enough to have noticeable effect on the captureprobability. The phase time was then increased so as to probe the time constant parameter space.To ensure that dipoles were correctly identified, first a background signal subtraction was takenfrom each adjacent pair of pixels and then the intensity differences for each pair were calculated.A threshold was set such that only sufficiently intense (>500 h+) dipoles were further analysed. Anumber of subsequent checks were then made to reduce the number of false positives, where noiseor the cumulative effects of multiple defects could lead to over-estimation of defect densities.

An area of 1000 rows by 500 columns was analysed for both irradiated regions as well as acontrol region. Table 1 gives the estimated defect density values for each defect species in bothirradiated sections of the device as well as the control section, where each density value is anaverage of the number of defects across the three corresponding temperatures. These values do notrelate to the true number of defects within the lattice but instead the number that can be assumed tointeract with a signal charge cloud of this size (25000 h+). Density values have also been doubledsince the method of trap pumping only reveals defects beneath barrier phase-electrodes [13]. It canbe seen in Table 1 that the defect densities scale consistently with the radiation fluence.

Table 1: Trap densities for each region of the device.

Control 2×109 p+cm-2 4×109 p+cm-2

Ci (1.07±0.05)×10−3 pix-1 (9.22±0.15)×10−3 pix-1 (1.54±0.02)×10−2 pix-1

VV (1.66±0.06)×10−3 pix-1 (1.95±0.02)×10−2 pix-1 (4.60±0.03)×10−2 pix-1

4.2 Emission Time Constants

Once dipoles were identified the intensity curves were produced and fit with a curve correspond-ing to Equation 3.1. Curves were fitted using the Nelder-Mead method to perform an unconstrained,non-linear minimization of the sum of squared residuals with respect to the various parameters [19].Figure 2 shows several of the intensity curves for each defect species; it was observed that for alarge number (~50%) of the carbon interstitial defects the intensity curve was inverted such that theemission time constant is proportional to the phase time at a minimum of the curve rather than amaximum. This did not appear to affect the time constants themselves; τe values calculated fromthe inverted curves are distributed equally with those calculated from the regular curves. Howeverthe inversion of the intensity curves was unexpected and is very intriguing since it appears that thecarbon interstitial defect in each case is pumping signal in anti-phase with a flat level of pumping

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Figure 2: Examples of the intensity curves produced for dipoles by varying the phase time tph.The top two curves show the expected behaviour, whilst the bottom two show examples of the“inversion” which was observed for many of the carbon interstitial defects.

which is time independent; to the best of our knowledge, this phenomenon is previously unreportedin the literature. Further study is required in this area to see if similar effects are observed in differ-ent devices. Any signal or field dependence of the flat level would also provide more information.

After fitting each intensity curve the emission time constants were obtained from the parametersof the fitted curves. For defects producing reliable curves at all three temperatures the emissiontime constant was plotted against temperature. To find reliable curves the Pearson correlationcoefficient was used, with a lower threshold of 0.95 for the divacancy defects and 0.80 for thecarbon interstitials (which in general produced less well defined intensity curves). Figure 3 showsthe resulting plots for each defect species in both irradiated sections of the device, with one linerepresenting one defect tracked across the three temperatures and the τe value estimated by Mostekalso shown [11]. It can be seen that for both defect species the calculated emission time constantsare in agreement with the values estimated in the Mostek study. Tables 2 and 3 give the meanvalues of τe as well as the standard deviation at each temperature for the divacancy and carbondefects respectively. Example histograms of the emission time constants are given in Figure 4 and

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show for the divacancy defect a Gaussian distribution. Since the carbon defects are less numerousthe distributions are less well defined; however they also appear to be following an approximateGaussian distribution.

Table 2: Emission time constants and standard deviation for divacancy defects at each of the threetemperatures.

−114◦C −119◦C −124◦C

τe (s) 2.12×10−5 3.79×10−5 6.54×10−5

Spread (s) 5.20×10−6 9.17×10−6 1.60×10−5

Table 3: Emission time constants and standard deviation for carbon interstitial defects at each ofthe three temperatures.

−93◦C −97◦C −101◦C

τe (s) 3.91×10−4 6.65×10−4 1.02×10−3

Spread (s) 1.75×10−4 3.16×10−4 5.07×10−4

4.3 Discussion

From Tables 2 and 3 and Figure 3 it is clear that there is still a large spread in τe; howeverthe parallel nature of the lines for each defect appear to show that this visible spread is genuinerather than the result of measurement uncertainties. Figure 4 shows τe for 100 of the divacancydefects and allows for a clearer view of the distribution. We would expect some spread in the datadue to the effects of nearby defects with much larger or smaller time constants, small temperaturefluctuations during the pumping cycles and also because of our approximation that charge captureis instant. Other sources could include a possible Poole-Frenkel type effect where the orientation ofthe electric field within a given pixel would reduce the energy required for generation events [20].We plan to test this in a further study through adjusting the clocking voltages and monitoring anyeffect on the spread in time constant data. Other possibilities include multiple lattice configurationsof the same defect; it is well known that lattice defects are often metastable [21], however the effectsof different configurations on time constants are not fully understood.

5. Conclusions

We have studied two defect species within a p-channel CCD using trap pumping. A simplemodel of the charge trapping process described by two exponential time constants has been utilisedto obtain emission time constant data for both the divacancy hole-trapping level and the carboninterstitial. We have shown that this method can lead to improvements in our knowledge of defectemission time constants, which are extremely valuable for use in radiation damage models andcorrection algorithms. We have found that for the case of the carbon interstitial defect many dipoleintensity curves have been inverted, showing evidence of time independent signal pumping forwhich there is currently no explanation. High resolution in the time constant data has also allowed

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Figure 3: Clockwise from top left - Emission time constants against temperature for; 6677 diva-cancy defects in the heavily irradiated region, 2317 divacancy defects in the less heavily irradiatedregion, 911 carbon interstitial defects in the less heavily irradiated region and 1434 carbon intersti-tial defects in the heavily irradiated region. Each line corresponds to a single defect tracked acrossthree temperatures (3 data points on each line). The red lines show the emission time constant ofeach defect as estimated using the Mostek et al. energies and cross-sections [11].

us to observe a large amount of apparently genuine spread which exists for τe. It may be that we arelimited by genuine spread which could have many sources, several of which have been suggested.Further investigation into possible signal or field dependence of these effects is needed, as well asa more rigorous model of the capture process. A similar study on a much larger scale is plannedfor the near future using several n-channel devices both un-irradiated and after irradiations usingprotons, electrons, heavy ions and gamma rays. We aim to build upon the work carried out in thisinitial study to both provide highly accurate time constant data for relevant charge-trapping defectsacross a larger temperature range, as well as investigate further some of the current unknowns to

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Figure 4: Left - Histograms of the emission time constants for divacancy defects at -124 ◦C (top)and carbon interstitial defects at -101 ◦C. The shape and spread of the distributions, particularly inthe carbon interstitial case, are not clearly understood and will be an interesting avenue of furtherstudy once we have many more defects for analysis. Right - The emission time constant againsttemperature for 100 randomly selected divacancy traps, shown to outline the parallel nature of thelines for each individual defect.

build a clearer picture of the charge-trapping process. There is also the potential for the combinationof this technique with a model of charge-packet volume within a CCD pixel; in order to model thenumber of relevant defects which will interact with a charge-packet for a given set of conditionssuch as signal level, radiation dose, temperature and CCD operating parameters.

Acknowledgments

With thanks to ESA for providing the devices used during this study.

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